### 2.2.3.1 Evacuating a vessel to 10-8 hPa with a turbopumping station

A vessel made of bright stainless steel is to be evacuated to a pressure $p_b$ of 10-8 hPa in 12 hours. As can be seen from Chapter 1.3, there are other effects to consider in addition to the pure pump-down time for air. Both desorption of water vapor and adsorbed gases as well as outgassing from seals will lengthen the pump-down time. The pump-down times required to attain the desired pressure of 10-8 hPa are comprised of the following:

$t_1$ =Pump-down time of the backing pump to 0.1 hPa

$t_2$ = Pump-down time of the turbopump to 10-4 hPa

$t_3$ = Pumping time for desorption of the stainless steel surface

$t_4$ = Pumping time for outgassing the FPM seals

The desired base pressure $p_b$ sis comprised of the equilibrium pressure caused by gas flowing into the vessel through leaks and permeation $Q_l$ , as well as by gases released from the metal surface $Q_{des,M}$ and the seals $Q_{des,K}$:

$p_b=\frac{Q_l}{S}+\frac{Q_{des,M}(t_3)}{S}+\frac{Q_{des,K}(t_4)}{S}$

Formula 2-13: Base pressure of a vacuum system

 $p_b$ Base pressure [Pa] $Q_l$ Gas flow through leaks and permeation [Pa m3 s-1] $Q_{des,M}$ Outgassing from the metal surface [Pa m3 s-1] $Q_{des,K}$ Outgassing from the seals [Pa m3 s-1]

The vessel has the following data:

 $V$ Vessel volume 0.2 m3 $A$ Vessel surface 1.88 m2 $A_k$ ealing surface of the FPM seal 0.0204 m2 $Q_l$ 1.0 ⋅ 10 -9Pa m3 s-1 $q_{des_M}$ Area-related desorption rate of stainless steel 2.7 ⋅ 10 -4Pa m3 s-1 m-2 $q_{des_K}$ Area-related desorption rate of FPM 1.2 ⋅ 10 -4Pa m3 s-1 m-2

The backing pump should evacuate the vessel to 0.1 hPa in $t_1$ of 180 s, and should also be able to achieve this pressure with the gas ballast valve open. The volume flow rate can be obtained in accordance with Formula 2-9:

$S_{backing pump}=\frac{V}{t_1} \cdot \mbox{ln} \frac{p_0}{p_1} = 10.2 l s^-1 = 36.8 h^-1$

We select a Duo 35 with a pumping speed of $Sv$ = 35 m3 h-1.

The turbomolecular pump should have approximately 10 to 100 times the pumping speed of the backing pump in order to pump down the adsorbed vapors and gases from the metal surface. We select a HiPace 700 with a pumping speed $S_{HV}$ of 685 l s-1. Using Formula 2-9 we obtain

$t_2=\frac{V}{S_{turbopump}} \cdot \mbox{ln} \frac{p_1}{p_2} =2.0 s$

### Desorption from the surface of the vessel

Gas molecules (primarily water) adsorb on the interior surfaces of the pressure chamber and gradually vaporize again under vacuum. The desorption rates of metal surfaces decline at a rate of $t^-1$ ab. Time constant $t_0$ is approximately 1 h.

Using Formula 1-32 from Chapter 1

$Q_{des}=q_{des} \cdot A \cdot \frac{t_0}{t_3}$

we calculate the time taken to attain the base pressure

$p_{b3}=1.0 \cdot 10^-6 Pa$

$t_3=\frac{q_{des,M} \cdot A \cdot t_0}{S \cdot p_{b3}}=2.67 \cdot 10^6 s=741 h$

The resulting time of 741 hours is too long. The process must be shortened by baking out the vessel. The bakeout temperature is selected so as to prevent harming the most temperature-sensitive of the materials used. In our example, the temperature is restricted by the use of FPM seals which can easily withstand a temperature of 370 K. The desorption speed will be increased theoretically by more than a factor of 1,000 as a result [22]. And the bake-out time will in effect be shortened to several hours.

High desorption rates can also be lowered by annealing the vessel under vacuum or by means of certain surface treatments (polishing, pickling).

Since many pre-treatment influences play a role, precise prediction of the pressure curve over time is not possible. However in the case of bake out temperatures of around 150°C, it will suffice to turn off the heater after attaining a pressure that is higher by a factor of 100 than the desired base pressure. The desired pressure $p_{b3}$ ill then be attained after the vacuum chamber has cooled down.

### Seal desorption

The outgassing rates of plastic are important if operation is at temperatures of below 10-6 hPa. Although the surface areas of the seals are relatively small, desorption decreases only according to the factor

$\frac{t_0}{\sqrt{t_4}}$

given in Formula 1-33 in Chapter 1.

The reason for this is that the escaping gases are not only bound on the surface, but must also diffuse out of the interior of the seal. With extended pumping times, desorption from plastics can therefore dominate desorption from the metal surfaces. The outgassing rate of plastic surfaces is calculated according to Formula 1-33 in Chapter 1.

$Q_{des,K}=q_{des,K} \cdot A_d \cdot \frac{t_0}{\sqrt{t_4}}$

We use $Q_{des,K} = S \cdot p_{des,K}$ and obtain the following for

$p_{b4}$=10-8hPa: $t_4$=459 ⋅ 106 s = 1277 h.

In this connection $t_0$ = 3600 s and the associated value $q_{des,K}$ is read from the chart [23] for FPM. It can be seen that the contribution to pump-down time made by desorption of the cold-state seal is of a similar order of magnitude as that of the metal surface.

Since the diffusion of the gases released in the interior of the seal will determine the behavior of the desorption gas flow over time, the dependence of diffusion coefficient $D$ upon temperature will have a crucial influence on pumping time:

$D=D_0 \cdot \mbox{exp} \left(-\frac{E_{dif}}{R \cdot T} \right)$

Formula 2-14: Diffusion coefficient (T)

As temperature rises, the diffusion coefficient increases as well; however it will not rise as sharply as the desorption rate of the metal surface. As a result, we see that elastomer seals can have a pronouncedly limiting effect on base pressure due to their desorption rates, which is why they are not suitable for generating ultra-high vacuum.

### Leakage rate and permeation rate

The gas flow that enters the vacuum system through leaks is constant and at a given pumping speed results in a pressure of:

$p_{leak}=\frac{Q_{leak}}{S}$

A system is considered to be sufficiently tight if this pressure is less than 10% of the working pressure. Leakage rates of 10-9 Pa m3 s-1 are usually easy to attain and are also required for this system. This results in a pressure component of the leakage rate of $p_{leak}$ = 1.46 · 10-11 hPa. This value is not disturbing and can be left out of consideration.

Permeation rates through metal walls do not influence the ultimate pressure that is required in this example; however diffusion through elastomer seals can also have a limiting effect on base pressure in the selected example.

### Summary

Pressures of up to 10-7 hPa can be attained in approximately one day in clean vessels without the need for any additional measures.

If pressures of up to 10-4 hPa are to be attained, the pump-down times of the backing pump and the turbo-pump must be added together. In the above-mentioned case, this is approximately 200 s. At pressures of less than 10-6 hPa, the turbomolecular pump is required to have a high pumping speed, particularly in order to pump down the water desorbed from the metal walls.

This will only be possible by additionally baking out the vacuum vessel (90 to 400°C) if the required base pressure pb of 10-8 hPa is to be attained within a few hours. The heater is turned off after 100 times the value of the desired pressure has been attained. The base pressure will then be reached after the vacuum vessel has cooled down.

At pressures of less than 10-8 hPa, only metal seals should be used in order to avoid the high desorption rates of FPM seals.

Leakage and permeation rates can easily be kept sufficiently low in metal vessels at pressures of up to 10-10 hPa.